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d(P)
A.derivation(x)
A.derivation(y)
A.derivation(z)
A.derivation([2, z, x^2+y^2])
M.category()
Dx.bracket(Dy)
d.bracket(Dx)
A.fraction_field()
A.derivation_module(B)
A.hom([QQ(0)
QQ(1)
QQ(2)
A.derivation_module(ev)
M.gens()
M.gen(0)
M.gen(1)
M.gen(2)
Dx(f)
at (0,1,2)
Dy(f)
at (0,1,2)
Dz(f)
at (0,1,2)
B.hom([B(y)
B(z)
B(x)
B.derivation_module(twist=theta)
Field (twisting morphism: x |--> y, y |--> z, z |--> x)
M.gen()
d(x)
d(y)
d(z)
d(x + y + z)
Caruso (2018-09)
Copyright (C)
RingDerivationModule(Module, UniqueRepresentation)
__init__(self, domain, codomain, twist=None)
A.derivation_module()
TestSuite(M)
run()
GF(5)
GF(25)
GF(7)
RingDerivationModule(R5, R25)
RingDerivationModule(R5, R5^2)
Traceback (most recent call last)
RingDerivationModule(R5, R7)
Traceback (most recent call last)
R5.hom([R5.gen()
RingDerivationModule(R5, R25, twist=theta)
RingDerivationModule(R7, R7, twist=theta)
Traceback (most recent call last)
Rings()
Commutative()
TypeError("the domain must be a commutative ring")
Rings()
Commutative()
codomain.has_coerce_map_from(domain)
codomain.coerce_map_from(domain)
elif (isinstance(codomain,Map)
codomain.category_for()
is_subcategory(Rings()
codomain.domain()
has_coerce_map_from(domain)
codomain.domain()
codomain.domain()
coerce_map_from(domain)
defining_morphism.codomain()
not (isinstance(twist, Map)
twist.category_for()
is_subcategory(Rings()
TypeError("the twisting homomorphism must be an homomorphism of rings")
twist.domain()
twist.domain()
coerce_map_from(domain)
twist.codomain()
codomain.coerce_map_from(twist.codomain()
domain.gens()
twist(g)
defining_morphism(g)
except (AttributeError, NotImplementedError)
rings (with non free modules of derivations)
domain.is_field()
elif (domain is ZZ or domain in NumberFields()
FiniteFields()
isinstance(domain, IntegerModRing_generic)
or (isinstance(domain, pAdicGeneric)
and (domain.is_field()
domain.absolute_e()
elif (isinstance(domain, (PolynomialRing_general, MPolynomialRing_base, PowerSeriesRing_generic, LaurentSeriesRing)
or (isinstance(domain, FractionField_generic)
isinstance(domain.ring()
RingDerivationModule(domain.base_ring()
self._base_derivation.gens()
domain.gens()
tuple(self._base_derivation.basis()
domain.gens()
tuple(self._base_derivation.dual_basis()
domain.gens()